Markets for Other People’s Money: An Experimental

Study of the Impact of the Competition for Funds

February 20, 2012

Abstract

In this paper we experimentally investigate the impact that competing for fundshas on the risk-taking behavior of laboratory portfolio managers operating under thetypical contractual arrangements offered to hedge fund managers. We find that sucha competitive environment and contractual arrangement lead, both in theory and inthe lab, to ineffi cient risk taking behavior on the part of portfolio managers. Wethen study various policy interventions, obtained by manipulating various aspects ofthe competitive environment and the contractual arrangement of fund managers, e.g.,the transparency of the contracts offered, the risk sharing component in the contractlinking portfolio managers to investors, etc. While all these interventions would induceportfolio managers, at equilibrium, to effi ciently invest funds in safe asssets, we findthat, in the lab, transparency is most effective in incentivising managers to do so.Finally, we document a behavioral "Other People’s Money" effect in the lab, wherefund managers tend to invest the funds of their investors in a more risky manner thantheir own money, even when it is not in the investors’ interest nor in the managersincentives to do so.

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1 Introduction

One issue of prominence these days is what many consider to be an excessive amount of risk

taking in financial markets. What distinguishes these markets from others is the fact that in

these markets portfolio managers must compete for the right to invest other peoples’money.

In this paper we experimentally investigate the impact that competing for funds has on the

risk-taking behavior of laboratory portfolio managers operating under the typical contractual

arrangements offered to hedge fund managers. We construct a simple laboratory market for

capital among portfolio managers where each manager offers a contract that shares a stylized

version of various features that are commonly observed in real-world hedge fund markets.

More precisely, the investor is not well-diversified across funds, the hedge fund manager’s

investment strategy is opaque, and the managerial contract is characterized by option-like

compensation scheme according to which the manager receives (most of) the compensation

only for returns in excess of pre-specified strike price (the details of this contract are described

in Section 1.2).

In the simple model underlying our experiment, excessive risk taking is a feature of the

equilibrium: the interaction between the competition for funds and the option-like contract

for the manager leads to a result that no one desires. Different policy interventions aimed at

limiting risk taking on the part of managers do, in theory, rectify this outcome. We investi-

gate several of these, attempting to manipulate independently the competitive environment

of fund managers and their contractual arrangements. More specifically, in one intervention

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(the Transparency treatment) we manipulate the competitive environment of fund managers

by imposing transparency on their investment strategy; that is, by forcing the manager to

announce (and commit to) the risk level of its intended investment before the investor invests.

In a second intervention (the Risk Sharing treatment), we modify the managerial contractual

incentive compensation scheme to require complete risk sharing between the manager and

the investor. Finally, in a third intervention (the Restricted Competition treatment), we

also act on the managers’contractual arrangement by capping the strike price or promised

return which managers can offer investors to limit how much competition could unravel.

In all these environment, at equilibrium, portfolio managers should effi ciently invest

funds in safe assets. Indeed, all of these interventions prove to substantially reduce risk

taking in the experimental data. In particular, we find that the most effi cient intervention

in this respect is the Transparency treatment. However, these interventions fail to reduce

risk taking completely or as thoroughly as predicted by the theory.

One explanation for the failure of our policy interventions to completely eradicate exces-

sive risk taking may be that in these markets hedge fund managers compete for and invest

other people’s money and do so with little risk to themselves. Hence, from a behavioral point

of view, the fact that our laboratory managers are not investing their own money may lead

to a decrease in their level of risk aversion and a greater tendency to invest in risky projects.

To investigate this hypothesis, we ran an "Own Money" treatment, which is identical to the

Risk Sharing treatment except that in the OwnMoney treatment the manager is investing his

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own funds while in the Risk Sharing he is investing other people’s money that he competed

for. Interestingly, we find that managers tend to invest other people’s money in riskier assets

than they invest their own money. We interpret this difference as a manifestation of what

we call the Other people’s money effect.1 Indeed, while managers invested their own funds

in the risky project only about 10.2% or 21.5% of the time (depending on the treatment),

they invested other people’s money in such projects 42% of the time in the Risk Sharing

treatment. The Other peoples’money effect, therefore, represents a quantitatively significant

behavioral ineffi ciency induced by competition for funds in our hedge fund laboratory.2 In

other words, the excessive risk taking we observe in this paper may stem from two sources.

One is the natural result of competition in which excessive risk raking is a feature of the

equilibrium. On top of this, however, may be an Other people’s money effect where subjects

behave in an excessively risky way because they are not investing their own money.

Our paper, adds to the literature in a number of ways. To begin with, we are one of

the few (if not the only) papers that look at an evironment where contractual arrangements

interact with various aspects of competition in a financial market. For example, others have

investigated the impact of contracts on the behavior of agents in financial makets; see, e.g.,

Levitt and Syverson (2008), who look at contracts in real estate markets; and Ou and Yang

1After the title of the 1991 Norman Jewison movie, with Danny De Vito.2The Other people’s money effect is consistent with the fact that hedge fund performance appears to be

positively linked only to measures of the overall pay-performance sensitivity of managerial incentive pay (theoverall "delta"), which include private ownership; see Agarwal-Daniel-Naik (2008). While private ownershiprequirements are included in incentive contracts to align the manager’s and the investors’objectives, theymight also have the effect of limiting the Other people’s money effect.

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(2003), Palomino and Prat (2003), He and Xiong (2010), and Chevalier and Ellison (1999),

who investigate contracts for portfolio managers. None of these papers however integrate

competition into their models, studying instead one person contracting environments. With

respect to our Other peoples’money effect, there are a few related papers that study exper-

imentally the risk attitudes of subjects towards other people’s money. Brennan-Gonzales-

Guth-Levati (2008) investigates the relation between risk preferences and other-regarding

concerns when one’s own and another person’s payoff is risky. The main finding of this pa-

per is that behavior depends mostly on the riskiness of the subjects’own payoff and not so

much by the riskiness of the others’payoff. Chakravarty-Harrison-Haruvy- Rutstrom (2011)

examines risk attitudes of laboratory subjects towards their own uncertain payoffs as well

as the uncertain payoffs of other subjects. The major finding is that, when subjects make a

decision on behalf of an anonymous stranger, the chosen lottery (action) tends to be more

riskier than the lottery they would choose for themselves, controlling for preferences and for

beliefs about the preferences of others. While the experimental environments are very differ-

ent, the phenomena studied in this last paper and our own are related and are both referred

to as Other peoples’money effect. The main difference, however, is that in the Chakrvarty

et al. paper the decision makers who makes decisions for others are not incentivized to do

so while in our paper people make decisions for others under a variety of different incentive

contracts. Finally, Eriksen and Kvaløy (2010) find an opposite effect: agents handling other

peoples’money behave in a more loss-averse manner and take less risks for their clients.

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In this experiment, like Chakravarty-Harrison-Haruvy- Rutstrom (2011), managers have no

monetary incentives and act on their clients behalf strictly out of a sense of empathy and the

main manipulation is the frequency with which information is given to the subjects thereby

effecting how myopic their updating is.

1.1 What this paper does not do

Before we present our analysis it is important to state what we consider to be the main aim

of our experiment. First, while we present a simple model of the competition for funds, our

emphasis is not on the model’s point predictions. Rather, as is true in many experiments,

we are more interested in its qualitative comparative statics since it is those that have the

major policy implications. Second, while we couch our discussion with reference to the hedge

fund market, our interests are broader than that since our results hold for any market where

firms compete for funds.3

1.2 Hedge Funds

To put our experiments in their proper context let us discuss the market for hedge funds.

Hedge funds are largely unregulated investment funds which, in the last twenty years have

3With respect to hedge funds, one may argue that the terms of hedge fund contracts are not negotiated inthe market but rather set historically as a "2/20 contract" (2% fixed commission and an additional 20% if thehedge fund earns more than a threshold ("high water-mark") return). Our results are still highly relevant,however, since the question remains as to whether this contract provides incentives for prudent or riskyinvestment. In other words, this contract, while a current market norm, was presumably once historicallydetermined by competition and the question as to whether it was set effi ciently remains of relevance.

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become increasing important in the capital markets. At its peak in the summer 2008, the

hedge fund industry managed around $2.5 trillion, according to Aima’s Roadmap to Hedge

Funds, Inechen-Silberstein (2008).4 Hedge funds typically compete for institutional and

wealthy investors, requiring a substantial minimal investment tranche to participate in the

fund (thereby imposing substantial diversification costs to investors). Moreover, hedge funds

are characterized by their investment strategies and by the incentive schemes their managers

are compensated with.

The investment strategies and styles of hedge funds are generally opaque, and are not

revealed to investors. In other words, fund managers compete for investors in this market by

signalling skills through past performance and through their incentive compensation scheme.

Managers’ compensation includes typically a small management fee (proportional to the

investment tranche, of the order of 1 − 2%) and a larger performance fee, of the order of

15 − 25% of returns exceeding the "high-water mark" (the maximum share value in a pre-

specified past horizon). This incentive compensation scheme is equivalent to a call option

with the "high-water mark" as strike price. Furthermore, the manager is subject only to

limited liability, while it is relatively standard in the industry to require that a substantial

fraction of the managers’private capital be heavily invested in their own fund.5

Option-like contracts, like those common in the hedge fund industry, are designed to

4The first hedge fund was apparently founded by A.W. Jones, a sociologist and financial journalist, in1949. In the 1990’s, however, the industry was managing about $50 billions; see Malkiel-Saha (2005).

5See Fung-Hsieh (1999) and Goetzmann-Ingersoll-Ross (2001) for rich institutional details on the hedgefund industry.

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signal managerial skills,6 but also induce managers to take high risks.7 A large empirical

literature has documented that, in fact, i) hedge funds returns contain a significant excess

risk-adjusted return due to managerial skills (or "alpha"),8 ii) hedge fund returns are signif-

icantly riskier than other investment forms (e.g., mutual funds).9 In particular, even though

hedge fund returns display a low correlation with stock market indices, they are character-

ized by exceptionally large cross-sectional range and variation.10 Furthermore, the attrition

rate of hedge funds in the market is very high (over 50% in 5 years from the 90’s).11

We proceed in this paper as follows. In Section 2 we will present a simple model of a

market for capital and we prove some simple results about the equilibria of such markets.

The capital markets in the model share some features of the capital markets in which hedge

funds compete. The objective of the model, however, is to capture only some stylized features

of these markets, and hence we abstract from several institutional details which might affect

in a relevant manner the allocation of funds in these markets. We will then introduce, in

Section 3, our experimental design, mapping the model into a simple laboratory market. In

6See, however, Foster-Young (2008) for a theoretical result suggesting lack of separation along the skilldimension in these contractual environments.

7More precisely, a rational portfolio manager facing a dynamic option-like contract will be lead to takeextreme risk while the fund is below water (its return below the "high-water" mark), while he will investmore safely when just above water. See e.g., Carpenter (2000), Goetzmann-Ingersoll-Ross (2001), andJackwerth-Hodder (2006) for the supporting portfolio choice theory; but see also Panageas-Westerfield (2007)for different results with infinite horizon.

8See Edwards-Caglayan (2001).9See Brown-Goetzmann-Park (2001).10See Brown-Goetzmann (2001) and, especially, Malkiel-Saha (2005).11Even after accounting for survivor (and other related) bias, hedge funds paid (geometric) average returns

2% in excess of mutual funds in the period 1996−2003; see Malkiel-Saha (2005), Table 3−4. See also Liang(2000) and Amin-Kat (2002).

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Section 4 we present the results of our experiment. Finally, in Section 5, we present our

conclusions.

2 The market for Funds

The type of markets we are interested in are the capital markets in which hedge funds

compete for funds. In such markets typically,

i) the size of the investment per investor is fixed, say $1 (million, typically);

ii) the hedge fund manager receives a share, β, of all profits made above a "high-water

mark"/strike price, w;12 if the funds are lost, the hedge fund manager is not liable,

that is, he/she only shares the upside risk in the contract and not any downside.

iii) the fund manager is under no requirement to offer the investor any specific information

about her fund’s investment strategy.

More precisely, when β, and w are as described above and R is the return earned by the

fund in any given year, the cash flow accruing, respectively, to the investor (Πinvestor) and

12We abstract from small fixed fees, which possibly have little effect on risk taking in practice in hedgefund markets.

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the hedge fund manager (Πmanager) can be written as follows:

Πmanager = βmax(0, R− w)

Πinvestor = min(R,w) + (1− β) max(0, R− w)

2.1 Contractual environments (Interventions)

Consider a world with two hedge fund managers and one investor. The investor possesses a

$x-chip to be invested, which the managers compete for. The manager who is successful in

attracting the chip can invest it in one of two projects, called safe and risky.

The return on the safe project is a dichotomous random variable paying Rs > 0 with

probability 0 < ps < 1, and 0 otherwise. The return on the risky project is also a dichotomous

random variable paying Rr > Rs > 0 with probability 0 < pr < ps < 1, and 0 otherwise.

Note that the risky project, has a higher return when successful with respect to the safe

asset; but the probability of success is higher for the safe asset. We assume however that

the safe payoff has a higher expected return,

psRs > prRr

This assumption is called for, because we want to study the case in which investing in

the risky asset is a dominated choice, absent the moral hazard implicit in the hedge fund

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manager’s intermediation of funds.

We consider several alternative contractual environments (interventions) in which the

hedge fund managers compete for the investor’s funds. Each contract environment will serve

as a treatment in our experiment. To avoid considering a multi-dimensional competition

problem, we consider the following extreme cases.

1. Baseline (hedge fund) contract. In this contract β is fixed = 1 and the managers

compete for funds by choosing the water mark, w.

2. Risk Sharing contract. In this contract, in contrast to the hedge fund contract above,

w is fixed = 0 and managers compete by offering different shares β of the proceeds

of their investments.

3. Transparency contract. This contract is identical to the hedge fund contract (β = 1 and

managers compete by setting w), except that when competing for funds, the manager

is required to publicly commit to the project the funds will be invested in. (This

implicitly assumes the investment is verifiable).

Finally,we also study a contractual environment in which a legally binding condition

restricts the hedge fund managers’offers,

4. Restricted contract. This contract is again identical to the hedge fund contract (β = 1

and managers compete by setting w) except for the fact that we place an upper bound,

x̄, on the w′s that can be offered and hence require require w ≤ x̄

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In any of the contractual environments described, after observing either w or β, depending

on the contractual environment, the investor decides which manager to invest his funds ($x)

with. The manager, before knowing if she will receive the funds decides which project, safe

or risky, to invest them into. The manager who has received the funds will then go ahead

and invest them as decided. After all investment decisions are made, the cash flow is realized

and payoffs determined.

We specify these various contracts because we will be interested in how they affect the

performance of the market for other people’s money. As the propositions below indicate,

these contracts can have a significant impact on the risk taking of managers and the subse-

quent welfare of our agents.

2.2 Equilibria

We now study equilibria in the different contractual environments.13 We concentrate first

on the basic hedge fund contract, our baseline.

Result 1: In the Baseline contract, there exist a cutoff w∗ such that, if w ≥ w∗ each

manager has an incentive to invest the funds in the risky project (strictly so, if w > w∗).

In fact, w∗ is such that each manager is indifferent with respect to her investment, and

13See Matutes-Vives (2000) for a model of bank competition which resembles, along several dimensions,our laboratory hedge fund market.

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it satisfies

w∗ =psRs − prRr

ps − pr> 0

Result 2: In the Baseline contract, if one manager offers w1 and another manager offers

w2 such that w1 ≤ w∗ ≤ w2 and w2w1> ps

pr, then the investor will give his chip to the manager

who offered w2. Likewise, in the Transparency contract, if one manager offers (w1,safe)

while the other manager offers (w2,risky) and w2w1

> pspr, then the investor will give his chip

to the manager who chose the risky project.

These results state that if one manager chooses the safe project, the other manager has

an incentive to offer a high enough w and choose the risky project. That is, there exists

a risk premium (pspr) such that a rational investor will be willing to leave the safe project

for the risky one. In the transparency contract an investor is able to observe the contract

in which his funds will be invested. Thus, an investor demands a compensation of at least

w2 ≥ w1 · pspr for high risk. In the baseline contract, if w1 ≤ w∗ ≤ w2 then the investor can

infer that a manager that offered w1 will invest in the safe project and a manager that offered

w2 will invest in the risky project (see result 1). Sincepsprw∗ < Rr a deviation on the part of a

manager to the risky project is always feasible. This is the case under a regularity condition

bounding the relative return of the safe project, a condition satisfied by the parametrization

of the game we take to the lab.

It is now straightforward to show, by a Bertrand competition argument, that

Proposition 1: In the Baseline contract, at equilibrium, both hedge fund managers offer

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w = Rr and invest the funds in the risky project.14

Proposition 2: In the Transparency contract, at equilibrium, both hedge fund managers

offer w = Rs and invest the funds in the safe project.

Proposition 3: In a Restricted contract, with x̄ ≤ w∗, at equilibrium both hedge fund

managers offer w = x̄ and invest the funds in the safe project.

Proposition 4: In a Risk Sharing contract, at equilibrium both hedge fund managers

offer β = 0 and invest the funds in the safe project.

Note that these contracts lead to different results in the market. For example, under

the Baseline contract, competition forces w up to the level of Rr and all funds are invested

in the risky project. In all the other contracts, however, at the equilibrium the funds are

invested in the safe project with different equilibrium w’s in the Transparency and Restricted

contracts and β in the Risk Sharing contract. For example, in the Risk sharing contracts

where managers compete by offering 1 − β and where w = 0, the only equilibrium is one

involving both investors investing in the safe project and β = 0. In this contract the incen-

tives of the investors and managers are perfectly aligned so that the managers should invest

the investor’s chip as if he was investing his own money. In the Restricted contract funds

should be invested in the safe project since we restrict x̄ ≤ w∗.

14This result holds true more generally, when managers in hedge fund markets compete by choosing boththe share, β, of all profits made above a "high-water mark"/strike price, w, and the "high-water mark"/strikeprice, w itself; see Appendix 1.

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2.3 Parametrization

In our experiments we investigate one particular parametrization of this model. In this

parametrization the safe project has a cash flow of 7 tokens if successful, with probability

.9, (Rs = 7, ps = .9) while the risky project has a cash flow of 10 tokens if successful, with

probability .5, Rr = 10, pr = .5. Without loss of generality, if we restrict w to be in [0, 10] it

is easy to show that, in this parametrization, w∗ = 3.25 and all our assumptions are satisfied,

i.e., 6.3 = psRs > prRr = 5 and psprw∗ = 5.85 < Rr = 10. Given this parametrization we

have the following equilibrium predictions for our different contracts.

Table I: Equilibrium Predictions

Contract Investment β wBaseline Risky NA 10Risk Sharing Safe 0 NATransparency Safe NA 7Restricted Competition Safe NA x̄ ≤ 3.25

3 Experimental design

Our experimental design attempts to implement the market for funds outlined above.15 The

experiment was run at the experimental lab of the Center for Experimental Social Science at

New York University. Students were recruited from the general undergraduate population via

E-mail solicitations. The experiment lasted approximately 45 minutes and average earnings

were $20. Each different contractual environment represents a treatment in the experiment.

15See Appendix for the instructions.

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The Baseline treatment is the hedge fund contract environment, which we introduce first.

When subjects arrived at the lab they were divided into groups of three with two managers

and one investor in each group. The experiment consisted of 20 identical decision rounds.

In each round the investor was endowed with one "investment chip". Each round started

by each manager simultaneously selecting a promised w ∈ [0, 10]. The managers also choose

which project, safe or risky, they intend to invest in. The w’s are announced to the investor

in the market, but not the investment decision, which is kept private. After both managers

choose their w’s, the investor decides who to invest his chip with. The selected manager then

has the right to make the investment that she decided on. The other manager can make no

investment in this round. We ran our market with only one investor in order to maximize

competition and with only two managers in an effort to minimize the number of subjects

needed (and hence the amount of money required).

After the investment decisions were made the chosen project was played out and payoffs

determined. A successful investment in the risky project paid 10−w tokens to the manager

and w to the investor. A successful investment in the safe project paid max {0, 7− w} tokens

to the manager and min {7, w} tokens to the investor (the manager is not liable for any loses

imposed on the investor).

After each round, both managers observe the w chosen by the other and which manager

received the chip. In case the manager received the chip, she was also informed as to which

project the chip was invested in, the resulting cash flow, and whether or not she was able

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to pay the investor in this round. The investor was told whether or not he received his

payment and his profit in this round, but not which project the chip was invested in. The

experiment then moved into the next round where subjects were randomly matched into

new groups of 3 while retaining their role in the experiment, so that if a subject was an

investor (manager) in round 1 she retained that role over the entire 20 rounds. The identity

of subjects were anonymous so subjects could not identify their roles. This eliminated the

possibility of managers creating a reputation.

In addition to the Baseline treatment, we ran several other treatments each of which

replicated one of the different contractual environments described above. The first such

treatment is the Restricted treatment, for which we pick x̄ = 3. This treatment was run

to check our hypothesis that it is competition, and the heightened promises of returns it

encourages, that lead to risky behavior on the part of investors. Obviously, since 3 < 3.25 =

w∗, in this treatment we would expect all funds to be invested in the safe project. Otherwise,

our hypothesis that risk taking is an artifact of market competition pushing promised returns

above w∗ = 3.25 would be easily disproved. In this treatment all procedures were identical

to those of the hedge fund contract except for the restriction on w.

Our Transparency treatment is identical to the baseline hedge fund contract except for the

fact that in the first move of the game the managers not only choose w, but also commit on

a project to invest in. In other words, they choose a pair (w, Project) where Project∈ {safe,

risky} and each pair chosen by the managers is shown to the investor. The investor then

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chooses a manager to give his chip to and the rest of the round is played out as in the Hedge

Fund treatment.

Our fourth treatment is the Risk Sharing treatment. In this treatment w = 0 and man-

agers offer a share 1−β to the investor indicating what fraction of the returns investors will

receive if the project succeeds. If β = 0 then all the proceeds of the investments go to the

investor, while if β = 1 then the manager keeps all the proceeds for himself. This treatment

is conducted using private information (when making their choice investors observe only the

shares both managers propose) in an effort to isolate the impact of the contract on behavioral

and not confound it with transparency considerations.

In all four treatments discussed above when the experiment was over we surprised the

subjects by informing them that we wanted them to engage in one more decision. In this

decision we gave each of them a chip and asked them to invest it for themselves in either

the risky or the safe project. The chip was worth 10 times the value of the chip used in the

previous 20 rounds so this decision was a more valuable one and should indicate how subjects

would invest when investing their own money rather than that of others. This investment

opportunity was given to both subjects who played the role of investors and managers in

the experiment. We will refer to this part of the experiment as Own Money (big stakes)

treatment.

The Own Money (big stakes) treatment is similar to the "surprise quiz" round used by

Merlo and Schotter (1999). In this treatment subjects play for large stakes and do so only

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once after their multi-round participation in the experiment. The idea is that this one

large-stakes decision should be a suffi cient statistics for all they have learned during their

participation in the experiment.16

Finally, we ran an an additional Own Money treatment which we call the Own Money

(small stakes) treatment. In this treatment, all subjects participating in the experiment

performed the role of managers. In each round (20 rounds in total) the manager was endowed

with his/her own chip and faced the same two investment projects: safe and risky. The

task of the manager was to choose how to invest his/her own chip. After the investment

decisions were made the chosen project was played out, payoffs determined and shown to

the subjects. As before, a successful investment in the risky project paid 10 tokens and a

successful investment in the safe project paid 7 tokens.

The Own Money (small stakes) treatment is designed to replicate as close as possible the

main features of the Risk Sharing treatment with one modification: managers are investing

their own money ("investment chip") as opposed to the other people’s money (the chip

received from the investor). Indeed, similar to the other treatments, in the Own Money

(small stakes) treatment the game is repeated (20 decision rounds), the stakes are of the

same magnitude and, finally, subjects have no prior experience with the game being played.

Given the projects available, at equilibrium, managers invest their own funds in the safe

project. This is the case also, at equilibrium, for the Risk Sharing treatment, in which

16In this sense it is preferable to repeating the Own Money (small stakes) treatment 20 times since in thattreatment repetition may lead to boredom and false diversification.

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managers invest funds received from the investor, because the preferences of the manager

and the investor are completely aligned. Any difference we might observe in manager’s

behavior when they invest their own money and investors’money, will be interpreted as a

manifestation of the Other peoples’money effect described in the Introduction.

Our complete experimental design is summarized in Table II.

Table II: Experimental Design

Treatment Competition Information Number of subjectsBaseline unrestricted only w 33Restricted Competition w ≤ 3 only w 30Risk Sharing unrestricted only 1− β 45Transparency unrestricted (w,Project) 39Own Money (small stakes) none NA 23Own Money (big stakes) none NA 147

4 Results

Depending on the contractual environment, competition for funds might lead the market to

unravel, inducing investment in a risky project when a safe project dominates in terms of

expected returns. This is the case at equilibrium in the Baseline (hedge fund) contractual

environment. The first fundamental question of the paper, therefore is,

1. Does the outcome in the lab experiment fit the equilibrium prediction in the Baseline

treatment where all funds are invested in the risky project and w = 10?

On the other hand, all the other contractual environments we study experimentally pre-

dict that, at the equilibrium, managers invest in the safe project offering w’s that vary with

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the contract used. The competitive mechanism leading to this outcome is however different

in the different contractual environments. A natural question we ask, therefore, is if this

prediction is borne out in the experimental data?

2. Does the market in the Restricted, Transparency, and Risk Sharing treatments lead to

investment in the safe project? Does competition in these treatments manifest itself

as predicted by equilibrium?

The other fundamental question we address in the paper regards the existence of an Other

people’s money effect.

3. Do managers in the Own Money treatments tend to invest their own chip in a safer

manner than they invested investor’s money in the Risk Sharing treatment? Is there

a Other people’s money effect?

After establishing the effects of the competition on the risk taking behavior of managers,

we shall turn to investors. Our main question in this respect is

4. Do investors choose the manager to invest with rationally? Do they anticipate the rela-

tionship between the return they are offered and the managers’investment strategy?

4.1 Does the market unravel in the Baseline treatment?

In the Baseline (hedge fund) contract environment, at equilibrium, managers are expected

to offer the highest return w = 10 and invest in the risky project. The key element in this

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result is that competition for funds will force w above 3.25 at which point investing in the

risky project becomes rational for the manager. In contrast, in the Restricted treatment,

where w ≤ 3, no funds should be invested in the risky project. Hence, our theory implies

that it is competition that is responsible for risky investment since it succeeds in pushing w

above the critical threshold. If funds were invested in the risky project equally in these two

treatments, then the obvious conclusion would be that it is not competition that leads to

risky behavior but, perhaps, some type of risk seeking that arises especially when managers

are investing other peoples’money. The cleanest way to identify such market unraveling in

the Baseline treatment is to compare the outcome in this treatment and in the Restricted

treatment.

Figure 1: How often were chips received from investors invested in the risky project.

65%70%

30% 30%

0%

10%

20%

30%

40%

50%

60%

70%

80%

all periods last 10 periods

perc

enta

ge

Baseline treatmentRestricted Competition treatment

As Figure 1 indicates, in the Baseline treatment managers invested the funds they received

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in the risky project 65% of the time. In fact, this percentage increased to 70% over the last 10

periods of the experiment, indicating that learning increases investments in the risky project.

Note that this percentage is only 30% in the Restricted Competition treatment (where we

actually predict it should be 0%). Using theWilcoxon rank-sum test, we reject the hypothesis

that the observed sample of how risky managers are in the Baseline and the Restricted

Competition treatments come from the same population in all 20 rounds (p = 0.0060) as well

as in last 10 rounds (p = 0.0139).17 Despite the lack of total conformity to the quantitative

predictions of the theory, we still see that qualitatively that competition for funds does lead

to significantly more risky behavior on the part of investors, as is predicted.

A period-by-period analysis of the investment decisions of the managers who received the

fund to invest is even more striking. As we see in Figure 2, except for the very early rounds,

most managers in the Baseline treatment choose the risky project.

17To perform the Wilcoxon rank-sum test, we constructed one observation per manager, which indicateshow often a manager invested the chip received from the investor in the risky project. The results of the testdo not change if we take into account all the intended investments of a manager and not just the rounds inwhich he/she actually received the chip from the investor (p = 0.0077 for all rounds and p = 0.0182 for thelast 10 rounds).

23

Figure 2: How often managers that received the chip from the investors

invested it in the risky project, by period

0%

20%

40%

60%

80%

100%

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

periods

Baseline treatmentRestricted Competition treatment

A second fundamental equilibrium prediction in the Baseline treatment is that risk taking

on the part of managers is associated to high-return offers (high w’s) to investors. In fact,

in this environment the theory predicts that w will rise to Rr = 10. Qualitatively, all that

matters in order to observe risky behavior is that the observed w in the market rise above

w∗ = 3.25 since such high promised returns are expected to lead to risky investments. This

is once again the case in the lab data.

Figure 3 presents the period-by-period offers of returns, w, for those managers intending

to invest in the risky project and in the safe project.

24

Figure 3: Period-by-period offers of returns (w) in the Baseline treatment.

3

3.5

4

4.5

5

5.5

6

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20

period

Managers that chose Risky projectManagers that chose Safe project

Note that managers promised consistently, on average, more than 3.25. In the first 5

periods, we observe only 6.4% (7 out of 105) of offers w < 3.25. In the remaining 15 rounds

this number drops to less than 3%. Moreover, managers intending to invest in the risky

project offer on average higher returns than those intending to invest in the safe project:

managers that chose the risky project offer, on average, a return of 5.26 (5.43 in the last 10

rounds) and those that chose safe project offer, on average, 4.60 (4.84 in the last 10 rounds).

It should be clear from our discussion that while our subjects in the Baseline treatment

did not push the promised return up to their limit of 10, as predicted, they did consistently

push it above the threshold where risky behavior became rational. Of particular interest is

the fact that for those managers intending to invest in the risky project, there seemed to

25

be a great resistance to offering an w much above 7. Over all 20 rounds there are relatively

few subjects who offered a w higher than 7. Even amongst those managers who attracted

the chip we observe rarely a w above 7 (6 out of 220 cases, less than 3%). This may be true

for a number of reasons. For example, in the Baseline treatment there is a residual 30% to

35% of subjects who invested in the safe project. For those subjects promising more than 7

was a losing proposition and rarely done. Hence, a manager intending to invest in the risky

project may have believed that it was not necessary to offer more than 7 since there was a

good chance that he would be facing a safe investor who he believed would never offer more

than 7.

In summary, on a qualitative level we find that, as predicted, competition in the Base-

line treatment greatly increases the fraction of funds invested in the risky project and lead

consistently to promised returns above w∗ = 3.25.

4.2 Do Transparency and Risk Sharing contracts lead to safe in-

vestments?

From the equilibrium predictions of our theory we would expect that Transparency or Risk

Sharing contracts would eliminate risky investment. This would be the case for different

reasons, however. In the case of Risk Sharing, since w = 0, the incentives of the manager

and the investor are aligned. Since the safe project has a higher expected return, it is in the

interest of the manager to invest in it so all funds should be invested in the safe project.

26

In the Transparency case it is competition that insures safe investment since the only

equilibrium is one where both firms promise to invest safe and offer w = 7 and, at that return,

there exists no promised return that can induce the investor to want his chip invested in the

risky project. As a result, we would expect less risky investment in the Risk Sharing and

Transparency treatments than in the Baseline treatment.

Figure 4: How often the chip received from investors was invested in the risky project.

65%70%

30% 30%

17%13%

41% 43%

0%

10%

20%

30%

40%

50%

60%

70%

80%

all periods last 10 periods

perc

enta

ge

Baseline treatmentRestricted Competition treatmentTransparency treatmentRisk­Sharing treatment

Figure 4 indicates that these expectations are substantiated by our data. As we can see,

while subjects invested in the risky project 65% of the time over the 20 periods of the Baseline

treatment, the did so only 41% and 17% of the time in the Risk Sharing and Transparency

treatments respectively. The dramatic impact of transparency on the hedge fund contract

is noteworthy since it indicates that investors in the experiment prefer to have their funds

invested in the safe project and that the excessive risk taking in the Baseline treatment

27

might be ascribed to investors inability to control how their funds are being invested.

Our Result 2 implies that if one manager proposes to invest in the safe project while the

other proposes to invest in the risky project, as long as the promised return on the risky

project is more than psprtimes the promised return on the safe project (1.8 in our parame-

terization), the investor should prefer to invest his money in the risky project. Perhaps

one of the reasons why we see so much investment in the safe project in the Transparency

treatment is that while there is a significant premium for risky investment in this treatment

(see Table III below), it is not suffi ciently large to induce investors to want to go risky. For

example, note that in the Transparency treatment the mean w offered for investment in the

safe project over all periods (last 10 periods) was 4.43 (4.73) while the same w offered for

investment in the risky project was 5.54 (5.95). As we see, while this premium is statistically

significant18, it is not, on average, as high as needed to be suffi cient to make risky investment

preferred by investors.

18According to the Wilcoxon ranksum test, we reject the null hypothesis that the w’s offered for investmentin the safe and risky projects come from the same population for all 20 rounds (p < 0.01) as well as for thelast 10 rounds (p < 0.01).

28

Table III: Average offers of managers, by treatment

average win all rounds

average win last 10 rounds

Baseline treatmentinvestors that chose risky project 5.26 5.43investors that chose safe project 4.60 4.84Transparency Treatmentinvestors that chose risky project 5.54 5.95investors that chose safe project 4.43 4.73

average βin all rounds

average βin last 10 rounds

Risk Sharing Treatmentinvestors that chose risky project 64.3% 71.6%investors that chose safe project 63.7% 71.7%

Finally, note that in the Risk Sharing treatment, managers that intended to invest in

the risky and in the safe projects offered very similar shares of the proceeds to the investor:

about 64% in all 20 rounds and about 72% in the last 10 rounds (see Table III)19. Thus, the

investors could not infer from the promises made by managers whether their funds will be

allocated to the safe or to the risky project.

4.3 Is there an Other people’s money effect?

The Other peoples’ money effect postulates that managers, for some reason, tend to be

more willing to take higher risks when investing other peoples’than their own money. To

be precise, we define the Other people’s money effect as the difference in the risk taking

19Wilcoxon ranksum test cannot reject the hypothesis that shares offered by the managers who intendedto invest in the risky project come from the same population as the ones offered by those who intended toinvest in the safe project (p = 0.4948 in all 20 rounds and p = 0.9448 in the last 10 rounds).

29

behavior of managers in the Risk Sharing and Own Money treatments. In both treatments,

in fact, managers’incentives are completely aligned with those of investors and theoretically,

at equilibrium, we expect to see all funds invested in the safe project.

Table IV: How often funds were invested in the risky project,

in the Risk Sharing and the Own Money treatments

Risk SharingOwn Money(small stakes)

Own Money(big stakes)

round 1 to 5 36.7% 23.5%round 6 to 10 42.0% 21.7%round 11 to 15 46.7% 19.1%round 16 to 19 40.8% 16.3%round 20 43.3% 43.5%

Overall 41.7% 21.5%managers 10.2%investors 10.2%

Table IV presents the percentage of times subjects made risky investment in the Risk shar-

ing and the Own money treatments. In the Own Money (big stakes) treatment only 10.2% of

subjects (both managers and investors) invested their own funds in the risky project,20 while

they did so 41.7% of the time in the Risk Sharing treatment. In other words, if subjects

have learned anything over the course of the 20 rounds experiment it is that they want their

chip to be invested in the safe project when it is worth a lot of money.

Similar conclusions can be drawn from comparing the Risk Sharing and the Own Money

(small stakes) treatments. Except for the very last round, subjects are much more likely

20Recall that the Own Money (big stakes) treatment was performed at the end of each session afteranother treatment. There is, however, no significant difference in the behavior of either managers or investorsaccording to the the different treatments they previously played (by the test of proportions). Therefore, wepool together all the data from Own Money (big stakes) treatment and report them together.

30

to make risky investments when they allocate other people’s money (41.7%) than their own

(21.5%). Moreover, the fraction of risky investments monotonically decreases with experience

in the Own Money treatment, while it is not the case in the Risk Sharing treatment. The

last round of the Own Money (small stakes) treatment shows the end-game effect: in the

last round 43.5% of the managers chose the risky project, which is two times more than the

percentage of risky investments in the first 19 rounds where average is about 20%.21

Figures 5 and 6 below depicts the histograms and the cumulative distributions of the

riskiness of the managers’ investments in the Own Money (small stakes) and in the Risk

Sharing treatments.22

21End-game effects are often observed in the experiments on finitely repeated games. See, for instance,Reuben and Suetens (2009) and the references mentioned there for end-game effects in the repeated prisoners’dillemma game.22For each manager, one observation is the fraction of the times he/she invested funds in the risky project

over the course of 20 rounds.

31

Figure 5: How often managers chose risky project

in Risk Sharing and Own Money (small stakes) treatments0

.1.2

.3Fr

actio

n

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1

Own money treatment

0.1

.2.3

Frac

tion

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1

Risk­sharing treatment

Figure 6: Cumulative distributions of how often managers chose risky

project in Risk Sharing and Own Money (small stakes) treatments

0.2

.4.6

.81

0 .1 .2 .3 .4 .5 .6 .7 .8 .9 1

Risk­SharingOwn Money

Cumulative distributions

32

Figures 5 and 6 clearly show that managers were much more risky with the investors’

money than with their own. Indeed, 52.2% of the managers in the Own Money (small stakes)

treatment invested their own funds in the safe project 90% of the time or more. That is,

more than half of managers chose the risky project at most twice out of 20 rounds played

in the Own Money treatment. The same behavior is rare in the Risk Sharing treatment, in

which only 13.3% of the managers behave that way. According to Kolmogorov-Smirnov test,

we reject the hypothesis that the distributions of the riskiness of the managers’investments

are the same in these two treatments (corrected p = 0.022).

This evidence for the Other people’s money effect possibly suggests that something in the

nature of competing for funds leads managers to want to be take more risks, risks that they

obviously would not want to take if they were investing their own money. It is natural to

search for rationalizations of this effect in the realm of behavioral economics. For instance,

managers might place other people’s money in a different mental account than their own (see

Thaler (1985), (1999)). In this case, the Other people’s money effect we document would

be related to the House money effect discussed by Thaler-Johnson (1990) and Keasey-Moon

(1996).

33

4.4 How do investors behave?

In this section we discuss the behavior of investors. Our objective here is to understand

if the behavior of investors in our experimental data is also qualitatively consistent with

equilibrium. This is particularly apparent in the Transparency treatment, where the rational

action of investors is not confounded by their beliefs about which project the manager will

invest in. In this treatment, over all 20 rounds there were 172 cases where both managers

chose the same project. In 164 of these cases (95%), investors, as expected, gave their chip

to the manager offering the highest w. In 88 cases, one manager chose the risky project while

the other chose the safe one. In 7 of these cases the risky manager promised 1.8 more than

the safe one and in 5 of these 7 (71.4%), the investors gave their chip to the risky manager.

On the other hand, in 13 cases the safe manager promised more than the risky one and in

all 13 cases (100%) the investors gave the chip to the safe manager. Finally, in 68 cases the

manager offering a risky investment promised more than the one offering a safe investment

but less than 1.8 times more. Here the chip should go to the safe manager and it did so 58

out of 68 cases (85.3%). All of these statistics are supportive of the hypothesis that investors

behaved as we expected them to in the experiment. In all of these cases above (except for

the 5 out of 7 cases), using a binomial test, we can reject the hypothesis that the chip was

allocated randomly with a prob = 50%.23

23Over the last 10 periods the results are even stronger, albeit with fewer observations. More precisely,in 91 cases both managers chose the same project. In 89 out of 91 cases (98%), investors gave their chip tothat manager making the highest promised w. In 39 cases, one manager chose the risky project and another

34

5 Conclusions

This paper has investigated the impact of competition on the risk taking behavior of labora-

tory hedge fund managers who operate under the standard hedge fund option-like compen-

sation contracts. We find that the competition for funds does indeed lead to an equilibrium

where funds are invested in an ineffi cient risky manner. This problem can be mitigated by

either changing the contract type, restricting the watermark used in the hedge fund contract

or by forcing managers to reveal the projects in which funds will be invested. While these

interventions are successful to a limited degree, they fail to completely eliminate the risky

behavior of managers due to their documented inclination to invest the money of others in

riskier assets than their own.

chose the safe one. In 2 of these cases the risky manager promised 1.8 more than the safe one and in both 2cases (100%), the investor gave the chip to the risky manager. In 6 cases the safe manager promised morethan the risky manager and in all 6 cases (100%) the investors gave the chip to the safe manager. Finally,in 31 cases, the risky manager promised more than the safe manager but less than 1.8 times more, and thechip went to the safe manager in 27 out of 31 cases (87.1%). Again, all of these facts are supportive of thehypothesis that investors behaved in a rational manner in our experiment.

35

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39

6 Appendix 1: A Note on Hedge Fund Contracts

As we described in Section 2, a typical hedge fund contract specifies a pair (w, β) whichrepresents a watermark w and a share β of profits above watermark that managers keeps forhimself. We will show below that,if β ≥ β̄ > 024 there exists an equilibrium in which all the funds are invested in the risky

project.

We will show that we can sustain an equilibrium in which both managers propose contractwith w = Rr, β ∈ [β̄, 1] and invest in the risky project.

First, similarly to the Result 1, if w > w∗ then a manager will prefer to invest in the riskyproject because

Πmanagerw,β,safe < Πmanager

w,β,risky ⇔ psβ(Rs − w) < prβ(Rr − w)

⇔ w > w∗ =psRs − prRr

ps − pr

Thus, when an investor gives his funds to a manager that promised w = Rr, his funds willbe invested in the risky project.

To sustain the equilibrium proposed above, the only deviation that we need to rule out is theone in which one of the managers proposes w = w∗ and β′ ∈ [β̄, 1]. If this proposal attractsthe investor, then it is clearly beneficial for the manager because it gives him/her positiveexpected profits, as opposed to the zero profits which is what he/she earns following strategyw = Rr and β ∈ [β̄, 1]. However, this deviation will attract the investor only if Πinvestor

w=Rr ,β <Πinvestorw=w∗,β′ . Thus, to rule out this deviation we need to make sure that Πinvestor

w=Rr ,β ≥ Πinvestorw=w∗,β′.

But:

pr ·Rr ≥ ps · [w∗ + (1− β′)(Rs − w∗)]⇔ β′ ≥ β∗ =psRs − prRr

ps(Rs − w∗)Thus if β∗ < β̄ then for any β′ ∈ [β̄, 1], there exists an equilibrium in which all the fundsreceived from an investor are allocated to the risky project.We interpret therefore the assumption that β = 1, which we adopted in the paper, as a

simplification of the analysis.

24In fact, in the hedge fund markets, managers typically keep 15−25% of returns exceeding the watermarks.Thus, we will focus on the situation in which this share β is bounded away from zero.

40

7 Appendix 2: Instructions for the Baseline Treatment

This is an experiment in decision-making. If you follow the instructions and make gooddecisions, you can earn a substantial amount of money, which will be paid to you at the endof the session. The currency in this experiment is called tokens. All payoffs are denominatedin this currency. The experiment consists of 20 identical decision rounds. At the end ofthe experiment, we will sum up the tokens you earned in all 20 rounds and this amount willbe converted into US dollars using a conversion rate of 10 tokens = $1. In addition, you willreceive a participation fee.

Before the beginning of the experiment you will be randomly assigned roles: 23of the par-

ticipants will be assigned a role of investors and 13of participants will be assigned a role of

lenders. The role of an investor will be to invest an "investment chip" if one given to himby the lender, while the role of the lender will be to decide whom to given his investmentchip to. Roles stay fixed until the end of the experiment. That is, if at the beginning of theexperiment you were assigned the role of an investor (lender) you will keep this role for all20 rounds.

In each round, participants will be randomly matched into the groups of 3 people. Each groupconsists of two investors and one lender. Once the round is over, you will be re-matchedwith other participants for the next round. However, there will always be two investors andone lender in every group. The investors will receive a participation fee of $10 and lenderswill receive a participation fee of $5.

Decision of the investors in each period.

Each period starts with the lender being given one chip which he/she will lend to one ofthe investors in their group. This chip has no value other than providing the right to geta return if it is invested, i.e. it cannot be converted to tokens. Investors are the ones whodecide how a chip received from the lender is invested and how many tokens the lender willreceive if the investment is successful.

There are two investment projects: Project 1 and Project 2, which differ in the returns andthe probability of defaulting:

• Project 1 pays back 10 tokens with probability 50% and 0 tokens with probability50%.

• Project 2 pays back 7 tokens with probability 90% and 0 tokens with probability10%.

41

In other words, Project 1 has a return of 10 tokens and 50% probability of defaulting.Project 2 has return of 7 tokens and 10% probability of defaulting.

Each period starts with the investors making two decisions. First, each Investor chooseshow many tokens he is willing to pay to the lender that lends him his/her chip in case theinvestment is successful. Second, each investor chooses a Project in which the chip receivedfrom the lender will be invested. The number of tokens that the investor can pay the lenderfor a chip can be any number between 0 and 10 tokens with one digit after decimal, i.e.numbers like 3.2, 4.6, 5.9, 8.6 etc... This number represents how many tokens an investorwill pay the lender that lends him his/her chip in case the project in which this chip wasinvested was successful. If the project in which the chip was invested defaulted, then boththe investor and the lender get zero tokens. Each investor makes his/her choice withoutknowing what the other investor from his group chose.

Decision of lenders in each period.

After both investors make their choices, the lender observes how many tokens each investorpromises to pay to the lender that gives him his chip. The lender’s task is to choose whichinvestor he/she is willing to lend his chip to. Notice that lenders do not observe whichproject the investor chose to invest in (project 1 or 2); they observe only the promises of theinvestors in their own group. The screen for the lenders will look like this

Investor A promised to pay back x tokens

Investor B promised to pay back y tokens

It is important to note that in each round, the lender is matched with different investors.Therefore, it is impossible to track the same investor between periods. For instance, aninvestor who appears as Investor A in one round is not the same person as investor whoappears as Investor A in the next round.

How the profits of the investors and the lender are determined.

In any period, an investor that did not receive a chip from the lender will receive zero tokensin that period.

If the investor who did receive a chip and promised to pay back x tokens, then

• if the project in which the chip was invested defaulted, both the investor and the lenderget 0 tokens in that period

42

• if the chip was invested in Project 1 and did not default, then the investor gets 10− xtokens in that period and the lender gets x tokens as promised.

• if the chip was invested in Project 2, did not default and x ≤ 7, then the investor gets7− x tokens in that period and the lender gets x tokens as promised.

• if the chip was invested in Project 2, did not default and x > 7, then the investor gets0 tokens in that period and the lender gets 7, which is less than what investor promisedto him.

Quiz.

Question 1

Say an investor that received a chip from the lender promised to pay back 7.3 tokens, in-vested this chip in Project 1 and Project 1 did not default. What is the profit of the lenderin this period? What is the profit of the investor that received the chip in this period? Whatis the profit of the other investor from the same group? What is the profit is each subjectin a group if Project 1 defaulted?

Question 2

Say investor that received the chip from the lender promised to pay him back 4.9 tokens,invested this chip in Project 2, which did not default. What is the profit of the lender inthis period? What is the profit of the investor that received the chip? What is the profit ofthe other investor from the same group?

Investor’s feedback.

At the end of each period investors observe the following information: how many tokenshe/she promised to pay back to a lender that lends him/her chip; how many tokens theother investor promised to pay back to lender; whether or not the investor received the chipfrom the lender; in case the investor received the chip from the lender, which project wasthe chip invested in and whether the project was successful or not; whether the investor wasable to repay the lender what he promised and profits of the investor in tokens. You will notbe told what project the other investor decided to invest in.

Lender’s feedback.

At the end of each period the lender observes the following information: how many tokenseach investor promised to repay to a lender that gives him his chip; which investor he/she

43

chose to lend the chip to and whether this investor was able to repay the promised return ornot. The lenders are also informed about how many tokens they received in this period.

To summarize:

• At the beginning of the experiment, subjects are assigned roles of investors and lenders,which they keep for the whole duration of the experiment.

• In each period subjects are divided into the groups of 3 people: two investors and onelender.

• Each period starts with the decision of investors as to how many tokens they promiseto repay to a lender that gives him/her an investment chip and which project, 1 or 2,the chip received from the lender will be invested in.

• The lenders observe the promised returns and choose one investor in their group tolend chip to

• The chip received by an investor is then invested in the project of his/her choice asdetermined at the beginning of the period

• Payoffs are realized and all lenders and investors observe how many tokens they receivein this period

• At the end of the experiment all tokens earned in these 20 periods will be summed upand their sum converted to US dollars at a rate of 10 tokens = $1. In addition, youwill receive a participation fee.

Last part of the experiment.

In this part of the experiment we will ask you all to act as an investor for one period andmake one investment decision with an investment chip which we will give you. Please choosewhether you want to invest in Project 1 or Project 2:

• Project 1 pays back 10 tokens with probability 50% and 0 tokens with probability 50%

• Project 2 pays back 7 tokens with probability 90% and 0 tokens with probability 10%

After you made your decision, we will roll a 10-sided dice to determine whether the projectyou invested in defaulted or paid back. If you invested in Project 1 and dice lands on 0, 1,2, 3 or 4 then Project 1 defaults and you get 0 tokens. If it lands on any number strictlyabove 4 (that is, 5, 6, 7, 8 or 9) then you get 10 tokens. If you invested in Project 2 and dice

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lands on 0 then Project 2 defaults and you get 0 tokens. If it lands on any other number (1,2, 3, 4, 5, 6, 7, 8 or 9) then you will get 7 tokens.

Amount of tokens you earn in this part will be converted into US dollars, using the conversionrate 1 token = $1, and added to your total payment.

Please circle the Project in which you want to invest your investment chip:

Project 1 Project 2

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